The pressure formula
Pressure is force spread over an area: P = F ÷ A, where F is force in newtons and A is area in square meters. A 100 N force on 2 m² produces 50 Pa. Smaller area means higher pressure for the same force. To find the force first, see the weight calculator.
Only the component of force perpendicular to the surface counts. A force applied at an angle presses less firmly than the same force applied straight on, so resolve it first if the direction is not square to the surface.
How to use this calculator
Enter the force in newtons and the area in square meters. The result is pressure in pascals (Pa), where 1 Pa = 1 N/m². Area must be greater than zero, otherwise pressure is undefined. Pair this with the work calculator for related mechanics problems.
Two unit traps catch people out. Masses in kilograms are not forces: multiply by 9.81 to get newtons first. And areas quoted in square centimetres must be divided by 10,000 to reach square metres — skipping that step inflates the pressure ten-thousandfold.
Worked example
A 100 N weight rests on a base of 2 m²: 100 ÷ 2 = 50 Pa. Halve the area to 1 m² and the pressure doubles to 100 Pa, because pressure rises as the contact area shrinks.
That inverse relationship explains a lot of everyday design. Snowshoes and wide tyres spread the same weight over more area to keep pressure low, while knife edges and drawing pins concentrate a modest force onto a tiny area to push pressure high enough to cut or pierce. Pressure is force spread over an area, so an accurate force is the first thing you need.
Frequently asked questions
- How do I calculate pressure?
- Divide the force by the area it acts on: P = F ÷ A.
- What are the units of pressure?
- Pascals (Pa), where one pascal equals one newton per square meter.
- Why must the area not be zero?
- Dividing by zero is undefined, so pressure has no value when area is zero.
- How does area affect pressure?
- For a fixed force, smaller area gives higher pressure and larger area gives lower pressure.
- How do I convert pascals to bar or psi?
- Divide pascals by 100,000 for bar, or by 6,894.76 for psi. One standard atmosphere is 101,325 Pa. Pascals are small units, so everyday pressures often run into the thousands or hundreds of thousands.